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The peg board, counted

Cara NevinEditor, board mechanics and operator documents, since 2026

Every slot, every probability, and the arithmetic to redo it

Nothing here is quoted from anyone

These figures come from no source at all. A board of n rows has 2^n paths, and the number of paths ending in each slot is a binomial coefficient — so the whole distribution can be written out exactly, for any board, by anyone with a calculator. Here it is for 8, 12 and 16 rows.

Ten operators whose records carry a house-games category, with the fields their own documents and licence registers actually publish. Every figure here is about the account, not about the board: nothing in this data says which games any of them carries, and no cell has been filled in to suggest otherwise. Every empty cell on this table is a list nobody read, and it is never a zero: a blank under coins does not mean an operator takes none, and a blank under countries barred does not mean it bars none.
OperatorLicenceCoins listedStudios listedAmount before ID checkCountries barredGo
Vaveour partnerCuraçao Gaming Authority · OGL/2024/1676/0905 · Active6Casino and sportsbook on one balanceCase by case, clause 8.7Open to this site’s readersVisit
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Wild.ioCuraçao Gaming Authority1280no amount published45
Bitcasino.ioCuraçao Gaming Authoritynot read1202,500 EUR1
RocketpotCuracao13not readUS$2,50034
RainbetAnjouan Gaming Board933no amount published11
Wolf.betGovernment of the Autonomous Island of Anjouan, Union of Comoros1332no amount published48
DuckDiceAnjouan Gaming Board1019no amount published16
FlushAnjouan Gaming Board985not readlist not read
BitslerCuraçao Gaming Authoritynot read41no amount published1
BitStarzCuraçao Gaming Authoritynot read62no amount published74

Why these numbers need no source

Everything below follows from one sentence: the ball makes one independent left-or-right decision per row, and the slot it lands in is determined by how many of those decisions were rights.

From that, the number of paths ending in a given slot is the number of ways of choosing which rows were the right-hand ones, which is a binomial coefficient. The total number of paths is 2 raised to the number of rows. A probability is the first divided by the second. That is the entire derivation, and it is unpacked more slowly on the page about the mechanism.

This is unusual on a gambling site and it is the reason this page exists. Almost every figure elsewhere in this subject is somebody's claim, traceable at best to a document. These are not claims. If a reader disagrees with a number below, the disagreement can be settled with a calculator in about a minute.

8 rows: 256 paths, 9 slots

Slots are numbered outward from the left edge. The table is symmetric, so slot 0 and slot 8 are identical, slot 1 and slot 7 are identical, and so on.

SlotPathsProbabilityRoughly
0 and 8 (edges)10.3906%1 in 256
1 and 783.1250%1 in 32
2 and 62810.9375%1 in 9.1
3 and 55621.8750%1 in 4.6
4 (centre)7027.3438%1 in 3.7

The nine path counts read 1, 8, 28, 56, 70, 56, 28, 8, 1, and they sum to 256.

12 rows: 4,096 paths, 13 slots

SlotPathsProbabilityRoughly
0 and 12 (edges)10.0244%1 in 4,096
1 and 11120.2930%1 in 341
2 and 10661.6113%1 in 62
3 and 92205.3711%1 in 19
4 and 849512.0850%1 in 8.3
5 and 779219.3359%1 in 5.2
6 (centre)92422.5586%1 in 4.4

The thirteen counts sum to 4,096.

16 rows: 65,536 paths, 17 slots

SlotPathsProbabilityRoughly
0 and 16 (edges)10.0015%1 in 65,536
1 and 15160.0244%1 in 4,096
2 and 141200.1831%1 in 546
3 and 135600.8545%1 in 117
4 and 121,8202.7771%1 in 36
5 and 114,3686.6650%1 in 15
6 and 108,00812.2192%1 in 8.2
7 and 911,44017.4561%1 in 5.7
8 (centre)12,87019.6381%1 in 5.1

The seventeen counts sum to 65,536.

Three things the tables say at a glance

The centre thins as rows are added. 27.34% at 8 rows, 22.56% at 12, 19.64% at 16. The ball is not less drawn to the middle; the middle has simply been cut into more pieces. The effect of the selector is worked through on the rows page.

A drawing of the meerkat tallykeeper holding a rack of glass tubes of different heights
The path counts for a 16-row board run 1, 16, 120, 560, 1,820, 4,368, 8,008, 11,440, 12,870 and back down again, and they sum to 65,536. Divide any one of them by 65,536 and you have that slot’s probability. These figures come from no source: a calculator settles any disagreement with them.

The edges collapse. One in 256 at 8 rows becomes one in 65,536 at 16 — a factor of 256 across a change that looks, on the screen, like moving a slider two notches. This is the arithmetic behind the very large multipliers printed at the ends of taller boards, which is taken apart on the multipliers page.

The bulk is narrow. On a 16-row board the three central slots take 54.55% of drops between them and the five central slots take 78.99%. Four fifths of outcomes land in under a third of the board's width.

What the tables are not

They are not a return-to-player figure. A probability distribution says how often each slot is reached; it says nothing at all about what any slot pays. Pair this distribution with one paytable and you get one expected return, pair it with another and you get another, which is exactly the swap the risk control performs on the risk levels page.

They are not a prediction about a run of drops. Each drop is independent, so a sequence of centre results makes the next result neither more nor less likely to be different.

And they are not advice. No slot, no row count and no risk setting is called good anywhere on this site, and the precision of this page is not an argument that any of them is.

Underneath the game sits an account

Once the ball has landed, everything that happens next is governed by documents rather than by arithmetic: what identity checks apply, how much can be withdrawn in a period, which countries an operator excludes. Those are read from the operators' own terms and licence registers and set out on the home page and on the verification page. How this site separates computed figures from quoted ones is on the methodology page.

Questions people type about the board

Are these odds the same at every casino?
The distribution across slots is, for any board with the same number of rows, because it follows from the row count alone. What differs between versions is the multiplier attached to each slot and the return to player the studio publishes. Probabilities are arithmetic; payouts are a design decision.
How likely is the top slot on a 16-row board?
One path in 65,536, which is 0.001526% of drops. Counting both outer slots together, it is 2 paths in 65,536, or one drop in 32,768. Those are the exact figures, not rounded estimates.
What are the odds of the centre slot?
19.64% on a 16-row board, 22.56% on 12 rows and 27.34% on 8 rows. The centre slot is always the single most likely one, and it becomes less dominant as rows are added because the same distribution is spread across more slots.
Can these odds be used to plan a session?
They describe one drop, and every drop is independent of every other. Nothing accumulates, nothing becomes due, and no sequence of past results changes the next one. This site publishes the distribution so that the picture matches the machine, and it recommends no way of using it.
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